His music is published by Southern Music Publishing Co., Shawnee Press, and TAP Music Publishing, and his music has been recorded by the CRI, Crystal, Coronet, Encore, and Albany labels. He coauthored, with John Ashmead, a book about the songs of Robert Burns.

Davison taught at Haverford College from 1959 until his death. He was survived by his wife, Elizabeth Davison.